@Neard122
You cannot take a pet reptile on a plane as baggage the way you can a pet dog or cat. They are not allowed, period.
You can ship through Ship Your Reptiles which is how I ship all my babies. Ship Your Reptiles uses FedEx. You cannot ship a reptile directly with FedEx--you have to go through someone like Ship Your Reptiles (there are a few other companies, but I use Ship Your Reptiles) who has a license with FedEx.
FedEx planes ARE set up to handle live animal shipping. They go in a box that is clearly marked as a live reptile. They are the last on the plane and go in a special compartment.
Your chameleon will have to be packed in a container inside the shipping box which you can buy from Ship Your Reptiles. You can also buy heating or cooling packs. I use Phase 22 packs, which freeze and thaw at 72F (22C) so they can both absorb heat (when they melt) or release heat (when they freeze). They are a lot more expensive (a little more than $4 each) than the usual ice packs but are more effective at keeping the animal in the correct temperatures. You would only need one for a small box, two at most. Ship Your Reptiles will sell you a single shipping box. They have a lot of information on their web site.
For a big chameleon like yours, you might have trouble finding some sort of solid deli cup that is big enough and will fit into a 7" x 7" x 6" box. You can use a paper bag stapled shut. Twist up some paper or paper towels into little ropes so the chameleon has something to grab onto and will keep the bag from collapsing. I don't ship in cloth bags as they have no structure and will collapse around the animal. I think it must be stressful for a chameleon to be wrapped up in a cloth bag. A good paper bag stapled shut is a very good option and would be my second choice if I couldn't find a plastic container that was big enough. A plastic container allows you to mist the chameleon and put in a damp paper towel so they will keep hydrated much more easily.
Since you are sending only one chameleon, you might want to buy a slightly bigger shipping box (9" x 12" x 6"). Take away about an inch and a half on each dimension for the Styrofoam lining and you get the inner dimensions. You can buy a ZipLock food container that will fit inside. Just drill holes in that. I've shipped adults like that with sticks secured through the sides so they have a little perch. It all depends on the size of the box since you don't want the animal to rub its back or nose.
I put two holes in each side of the outer box but it really depends on the temperature.
Have the animal shipped to a Ship Center and held at that facility for pick up. Not all FedEx locations will accept reptiles--only places that will accept dangerous goods will hold reptiles. I can help you find those locations as Ship Your Reptiles will as well.
I understand this is all very scary and upsetting but it will be okay. By all means contact me and I can help guide you through the process. Read all the guidelines on Ship Your Reptiles web site. It's a lot to digest the first time, but it is all common sense, really.